Phantom for production of controllable fMRI signal

ABSTRACT

The subject invention relates to a method and apparatus for producing stimulated MRI data. In an embodiment, a remote-controlled “smart phantom” can produce simulated data. The simulated data can be acquired from a MRI system. The subject device can generate control signals and send the generated control signals to secondary coils/probes placed in the subject smart phantom. The control signals determine the current flow in the secondary coils/probes, which act as local spin magnetization amplifiers and thus produce regions of variable contrast to noise ratio. The control signals can be generated with various parameters, such as BOLD models, different levels of contrast-to-noise ratio (CNR), signal intensities, and physiological signals. Comparisons can be made with the widely-used simulated data by computers. Validation of the subject smart phantom can be performed with both theoretical analysis and data of human subjects.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional Application No.60/508,570, filed Oct. 3, 2003.

The subject invention was made with government support under a researchproject supported by NIH grant no. RO1EB00974.

BACKGROUND OF THE INVENTION

Over the course of the past decade, a variety of neuroimagingtechnologies allow the structure and function of the intact brain to bestudied. This presents a tremendous opportunity to understand the humanbrain. Neuroimaging has the potential to reveal some of nature's mostclosely held and significant secrets, and informatics can assist inrealizing this potential.

As defined in Neuroimaging Informatics Technology Initiative (NifTI)2000 Workshop, “informatics, a computerized way to handle data, is usedto design and implement the manner in which the imaging instrumentscapture signals generated by the brain, as well as the behavioral tasksused to probe particular brain systems, reconstruct the resultingsignals, statistically analyze the data, and visualize the results”. Bythis definition, it is easy to find out that the informatics includes avariety of technologies, e.g., collection of data using new acquisitiontechniques (e.g. phase array coil), statistical analysis and processingof data, and visualization of data. However, the great potential ofinformatics in neuroimaging has been impeded by inadequate coordinationregarding the development and distribution of the informatics toolsneeded to meet this challenge. Existing informatics tools have beendeveloped separately, and now widely used software products are notadequately optimized for meeting the variety of needs of the broadercommunity.

There exist a strong need that the conclusions drawn from fMRI studiesregarding the relationship between functional activation signals andfunction of the brain should be based upon a clear understanding of themanner in which various tools affect the data at each stage ofprocessing. Knowing that the operations performed by informatics toolsare valid is important for interpreting the results of fMRI studies. Inaddition, comparing different tools to identify the conditions underwhich, and uses to which, they are best suited is significantinformation to both the researchers and clinicians. In this backgroundsection, some recent studies of fMRI activation simulation, statisticalanalysis tools, and parallel MRI reconstruction using phased array coilswill be briefly reviewed.

Simulation of fMRI Activation and BOLD Signals

After conception and implementation of any new neuro-imaging informaticstools, validation is an important step to ensure that the procedurefulfills all requirements set forth at the initial design stage.Manufacturer's physical phantoms were first used for this purpose.However, these are typically just static phantoms filled with water orgel. The informatics tools must be evaluated using a comprehensivevalidation that requires additional use of simulated data since it isvery difficult to establish ground truth with in vivo data. Experimentswith simulated data permit controlled evaluation over a wide range ofconditions, such as different Signal-to-Noise Ratio (SNR),contrast-to-noise ratio, and signal intensities. Such considerationshave become increasingly important with the rapid growth ofneuro-imaging.

Computer simulations of the Blood Oxygenation Level Dependent (BOLD)signals and neural activation have been developed by many researchers.In a recent publication (Sorenson, J. A. & Wang, X, ROC methods forevaluation of fMRI techniques. Magn. Reson. Med., 36:737-744 (1996)),the time course data was represented by a zero-baseline boxcar function.Gaussian noise was added to simulate physiologic “noise”, after whichthe data were convolved with a Poisson function to simulate hemodynamicssmoothing and delay. Also, structured noise in the form of slopes tosimulate signal drift and sinusoidal oscillations to simulaterespiratory motion were added. These simulated fMRI responses werefinally added to null data sets acquired on normal subjects, denoted as“human data”. In one study (Constable, R. T. et al. Quantifying andcomparing region-of-interest activation patterns in functional brain MRimaging: methodology considerations, Magnetic Resonance Imaging,16(3):289-300 (1998)), Gaussian-shaped activation signals were addedwith Gaussian distribution of white noise.

Another study (Morgan, V. L. et al. Comparison of functional MRI imagerealignment tools using a computer-generated phantom. Magn Reson Med.September 2001; 46(3):510-4) discussed the development of acomputer-generated phantom to compare the effects of image realignmentprograms on functional MRI (fMRI) pixel activation. The phantom is awhole-head MRI volume with added random noise, activation, and motion.It allows simulation of realistic head motions with controlled areas ofactivation. Without motion, the phantom shows the effects of realignmenton motion-free data sets. Prior to realignment, the phantom illustratessome activation corruption due to motion. A recent paper (Desco, et al.Multiresolution analysis in fMRI: sensitivity and specificity in thedetection of brain activation. Hum Brain Mapp. September 2001;14(1):16-27) presents a study that was undertaken to assess theperformance of different wavelet decomposition schemes by making use ofa “gold standard,” a computer-simulated phantom. As activation areas arethen known “a priori,” assessments of sensitivity, specificity, ROCcurve area, and spatial resolution can be obtained. This approach hasallowed the study of the effect of different factors: the size of theactivation area, activity level, signal-to-noise ratio (SNR), use ofpre-smoothing, wavelet base function and order and resolution leveldepth. Recently, a Functional Data Simulator has been provided by SENSORSYSTEMS (Medical Numerics, Inc., Sterling, Virginia) in their softwarepackage MEDx. This functional data simulator (MEDx) is a graphical toolfor constructing curves of signal intensity vs. time at a single pixeland then extrapolating to volumetric data. It can also be used to createsynthetic fMRI data for similar exploration of the effects of noise andtiming.

However, these studies, while providing a simulated activation signal,do not account for variations in the activation levels of differentpixels and are unable to depict accurately the temporal response of theactivation associated signal change. And the most important issue isthat these simulations do not account for the real MR imagingenvironment (non-stationary rather than stationary, or dynamic ratherthan static), spin characteristics and the noises introduced during thewhole imaging process, i.e. noises from MR power system, pre-amplifier,transmit/receive, and digitization (A/D) error.

By reviewing the literature, one can see that there are very limitedmeasurements, such as the signal-to-noise ratio or contrast-to-noiseratio, where static phantom (a simple container full of liquid) hasusually been used that provides static MR signals instead of dynamicsignal changes. As for the fMRI research, systematic comparison of theanalysis methods presented in fMRI cannot be conclusive if assessment isbased only on the highly variable activity of the human brain.Calibrated, repeatable fMRI signals are needed for a reliablevalidation.

Statistical Analysis of Activation

In recent years, a variety of advanced high performance informaticstools have emerged for statistical pattern mapping of functional dataand fMRI data visualization. Among them are the general-purpose fMRIanalysis packages, such as AFNI, Brain Voyager™, BrainTools, FIASCO,fmristat, iBrain, Lyngby, MEDx, scanSTAT, and Statistical ParametricMapping (SPM) as well as Special-purpose software packages, such as AIR,ANALYZE, ANIMAL, FreeSurfer, and SureFit. Qualitative characterizationsand comparisons have been done (Gold et al. Functional MRI statisticalsoftware packages: a comparative analysis. Hum Brain Mapp.1998;6(2):73-84, Lange et al. Staatistical procedure for fMRI. Chapter27 in Functional MRI, C. T. W. Moonen & P. A. Bandettini (Eds),Springer-Verlag (1999)). However, due to lack of a benchmark database,quantitative validation and comparisons of these tools are difficult andsometimes impossible.

The field of fMRI has been dominated by the notion of detectability ofactivation in a noisy background, and tremendous effort has been placedin the area of statistical signal detection methods. Among thesestatistical methods, some provide maps or images of descriptivestatistics, such as z-score, statistical t-test, General Linear Model(GLM), and Kolmogorov-Smirnov test. Generally speaking, all such mapsrepresent a ratio of the activation magnitude to the measured signalvariation.

Based on the differences in model, these techniques can be divided intotwo groups. The first is the parametric group. In general, parametricapproaches depend on assumptions about the possible parametric familiesof distributions generating the fMRI data. They attempt to determine thevalue of a parameter or parameter vector that identifies a particularmember among a large parametric family of plausible probabilitydistributions that generate the fMRI data. The parametric group includesfor example the statistical t-test, cross-correlation, and generallinear model (Friston et al. Statistical parametric maps in functionalimaging: A general linear approach. Human Brain Mapping, 2:189-210(1995), Worsley & Friston Analysis of fRMI time-series revisited-again.NeuroImage, 2:173-181 (1995)), uni-variate time series models, analysisin frequency domain, and longitudinal data analysis.

The second group is the non-parametric approaches, which make noassumptions about the possible parametric families of distributionsgenerating the fMRI data and are thus less dependent on a specificstatistical model. While this seems attractive, there is another side.If parametric assumptions are roughly correct, then a parametric,model-based approach is superior to one that does not employ theseassumptions. However, the difficulty is that it is usually difficult toknow the properties of the true data-generating mechanism, and somestatistical compromise between knowns and unknowns is often a pragmaticcourse of action. The non-parametric statistical procedures include, forexample, the Kolmogorov-Smirnov (KS) test, probabilistic analysis (Franket al., Probabilistic analysis of fMRI data, Magnetic resonance inmedicine, 39:132-148 (1998)), information-theoretic methods (Tsai etal., Analysis of functional MRI data using mutual information. SecondInternational Conference of Medical Image Computing andComputer-assisted Intervention, 1679:473-480 (1999); Zhao, et al. 2002Zhao, Q., Principe, J. C., Fitzsimmons, J., Bradley, M. M., Lang, P. J.(2001), “functional Magnetic Resonance Imaging Data Analysis withInformation theoretic Approaches”, “Biocomputing”, edited by PanosPardalos and Jose Principe, Chapter 9, pp. 159-174, Kluwer, 2002, andsome modern computational non-parametric statistics (e.g., permutation,jackknife and bootstrap procedure).

However, there is very limited published information about how varioustools affect the data at each stage of processing, what operationsperformed by informatics tools are valid, and under what conditions theyare best utilized. A standard procedure or ground truth is needed for anobjective characterization and comparison.

Establishing Ground Truth

Informatics tools are important both to performing neuro-imagingstudies, and to understanding the results. After conception andimplementation of fMRI informatics tools, validation is an importantstep to ensure that the procedure fulfills all requirements set forth atthe initial design stage. Though these tools must be evaluated on realdata, a comprehensive validation should ideally involve the additionaluse of simulated data with known parameters, since it is very difficultto establish ground truth with in vivo data. Qualitative analyses ofvarious informatics tools have been done using computer-simulatedfunctional activation signals. However, these computer-simulated dataare usually simply overlapped on top of anatomic images, they cannotreflect the real MR imaging process, such as the MR spin characteristicsand noises introduced during the process, i.e. noise from MR powersystem, pre-amplifier, transmit/receive, and digitization (A/D) error.Besides, due to lack of a highly characterized data set available to theresearch community, it is difficult to make an objective comparison ofthe fMRI informatics tools. A quantitative measurement tool is needed toprovide data that presents the MR imaging process, the ground truth, inorder to characterize and compare informatics tools.

Defining the Effect of Statistical Analysis Tools

Informatics tools are key to all stages of fMRI. However, there is verylimited published information about several fundamental aspects ofinformatics tools. These issues include a clear understanding of themanner in which various tools affect the data at each stage ofprocessing, the knowledge of under what conditions operations performedby informatics tools are valid, and comparisons of different tools toidentify the conditions under which they are best utilized.

Calibration of Different fMRI Experiments

Currently, numerous fMRI exams are conducted on various MRI scanners(e.g., General Electric Medical Systems, Siemens Medical Solutions,Philips Medical Systems) at different field strength (e.g., 1.5 T and3.0 T) and with different pulse sequences (e.g., EPI, Spiral), headcoils (e.g., birdcage, phased array) or protocols. With so manyvariables, comparison of the results become extremely difficult, makingit uncomfortable to share the findings from different research groups.Therefore, a calibration tool which acts as a reference or benchmark ofthe specific exam is highly needed to provide useful information forcomparison of the results.

Accordingly, considering all these problems, there is a need for aphysical fMRI simulation device or phantom. There is a need for a devicewhich can provide variable contrast of signals, with intensity changesfollowing the BOLD signals, and can allow the optimization of imagingprotocols. Also, there is a need for a device that can produce signals,such that the acquired signals from such a device can provide a goldstandard for characterization, validation and comparison of variousinformatics tools. Furthermore, there is a need for a physical phantomwhich can provide means for instantly checking system performance. Inaddition, there is a need for a device or phantom that can provide oneor more of the following features: a complete MR system and MR platformindependent; have complete control over timing or delays, signalintensity level, motion, and physiological “noise” such as cardiac andrespiratory signals; provide self-testing for quality control; and beeasy to use and transportable.

BRIEF SUMMARY OF THE INVENTION

The subject invention relates to a method and apparatus for producingsimulated fMRI data. In an embodiment, the subject invention pertains toa remote-controlled “smart phantom” that can produce simulated fMRIdata. In an embodiment, the simulated fMRI data can first be acquiredfrom a MI system. The subject device can generate control signals andsend the generated control signals to secondary coils/probes placed inthe subject smart phantom. The control signals can determine the currentflow in the secondary coils/probes by adjusting the impedance of thesecondary coils/probes, which can act as local spin magnetizationamplifiers and thus produce regions of variable contrast to noise ratio.The control signals can be generated with various parameters, such ashemodynamic response models and different levels of enhancement andphysiological noises. Comparisons can be made with the widely-usedsimulated data by computers. Validation of the subject smart phantom canbe achieved with theoretical analysis and/or with data of humansubjects.

The data associated with the use of the subject smart phantom can beused to establish a benchmark database, an Informatics Development andSupport Database for fMRI. This database can also be used to documentthe performance of registered informatics tools for storage with respectto the user-adjustable informatics parameters, the user-selected datasets processed, and the resulting visualization.

The subject smart phantom can enable quantitative and objectivecharacterization and comparison. For example, functional activationdetection can be investigated and compared among the general-purposeand/or other statistical analysis packages. Sensitivity and specificitycan be validated and compared by using the Receiver OperationCharacteristics (ROC) curve under different levels of signalintensities, CNR, spatial resolution, and physiological spectralbackground. Various methods of motion correction can be characterizedand compared using data acquired from accurately controlled motion ofthe subject smart phantom. Spatial and temporal filtering can also becharacterized and compared.

DETAILED DESCRIPTION OF THE FIGURES

FIGS. 1A-1C show a specific embodiment of a phantom in accordance withthe subject invention incorporating two planar rectangular loops.

FIG. 2 shows a schematic diagram of a loop of a quadrature secondarycoil incorporated with the phantom shown in FIGS. 1A-1C.

FIG. 3 shows a diagram of a specific embodiment of a smart phantomimplementation system in accordance with the subject invention.

FIG. 4A shows a circuit schematic in accordance with a specificembodiment of a coil and circuitry for incorporation with a phantom.

FIG. 4B shows a circuit schematic in accordance with a specificembodiment of a coil and circuitry for incorporation with a phantom.

FIG. 5 shows an embodiment of an implementation incorporating thesubject phantom in accordance with the subject invention.

FIGS. 6A and 6B show field distortions in the radial and longitudinaldirections, respectively, for a simulation of a cylindrical phantom offixed length in the z direction.

FIGS. 7A and 7B show a comparison of the field distortions for threeradius by moving the curves in FIGS. 6A and 6B, respectively, tocoincide at r=0 or z=0.

FIGS. 8A and 8B show an EPI (SLT=5 mm, TE=54, FOV=160 mm) image and aSpin-echo image (same slice, TR/TE=552/16) of a specific embodiment ofthe subject smart phantom acquired in a Siemens Symphony system.

FIGS. 9A and 9B show the field distortion for z=10 cm and z=35 cm,normalized at r=0 and the field distortion for z=10 cm and z=35 cm,scaled to make the overall change from r=0 to r=5 close to each other,respectively.

FIGS. 10A and 10B show an EPI image of an axial slice of an embodimentof a phantom in accordance with the subject invention and theBOLD-similar time course of the mean signal in the ROI with SNR=73,respectively.

FIG. 11 shows an embodiment of the subject phantom having a cylindricalshape and having a loop attached to each end of the phantom such thatthe axis of the cylinder intersects the centers of the two loops.

FIG. 12 shows a difference image from an ‘on’ state and and ‘off’ statefor a specific embodiment of the subject invention.

FIG. 13A shows the form a pulse pattern of an excitation RF magneticfield B₁, that can be used to excite a sample material in accordancewith an embodiment of the subject invention.

FIG. 13B shows the form of the rotating magnetization M of a samplematerial located in a static magnetic field B_(o) and excited with theexcitation RF magnetic field B₁ shown in FIG. 13A.

FIG. 13C shows the form of the induced RF magnetic field B₂ in a RF coilposition proximate to the sample material for which the rotatingmagnetization is shown in FIG. 13B, wherein the RF coil is decoupledduring the last portion of the plot.

FIG. 14A shows the form a pulse pattern of an excitation RF magneticfield B₁ that can be used to excite a sample material in accordance withan embodiment of the subject invention.

FIG. 14B shows the form of the rotating magnetization M of a samplematerial located in a static magnetic field B_(o) and excited with theexcitation RF magnetic field B₁ shown in FIG. 14A.

FIG. 14C shows the DC current that can drive one or more DC coilsassociated with a magnetic field parallel to the static magnetic fieldB_(o) to produce a static magnetic field opposed to field B_(o) oradditive with field B_(o), in accordance with an embodiment of thesubject invention.

DETAILED DISCLOSURE OF THE INVENTION

The subject invention relates to a method and apparatus for producingsimulated fMRI data. In an embodiment, the subject invention pertains toa remote-controlled “smart phantom” that can produce simulated fMRIdata. In an embodiment, the simulated fMRI data can first be acquiredfrom a MRI system. In this sense, the MRI data is data actually acquiredfrom a MR scanner, but the MRI data is referred to as “simulated” fMRIdata because it is not acquired from the dynamic activity of a patient.The subject device can generate control signals and send the generatedcontrol signals to secondary coils/probes placed in the subject smartphantom. The control signals can be used to adjust the impedance of thesecondary coils/probes so as to determine the current flow in thesecondary coils/probes, which can act as local spin magnetizationamplifiers and thus produce regions of variable contrast to noise ratio.

The subject invention can involve the placement of a sample material ina region of interest in a static magnetic field B_(o). The samplematerial in the static magnetic field B_(o) will have a magnetization M.One or more RF coils can be positioned in the static magnetic fieldproximate the sample material. For purposes of ease of description, thefollowing is a discussion of a single RF coil. The RF coil is associatedwith a magnetic field having a component perpendicular to the staticfield B_(o) in the region of interest. Of course, the magnetic fieldassociated with the RF coil changes direction as a function of positionand, as the static magnetic field B_(o) has a fairly uniform directionin the region of interest, the relative direction of the magnetic fieldassociated with the RF coil and the static field B_(o) will change as afunction of position as well. Preferably, the magnetic field associatedwith the RF coil is perpendicular to the static filed B_(o) in theregion of interest More preferably, the RF coil is planar and has anormal perpendicular to the static field B_(o). This discussion can beapplied to additional RF coils employed in multi-RF coil embodiments.

An excitation RF magnetic field B₁ is applied to the sample material soas to tilt the magnetization M of the sample material. Referring to FIG.13A, the excitation field B₁ can be applied as a series of pulses toform a pulse pattern. The RF coil can be decoupled during each pulse toreduce or eliminate fields that would be produced by the RF coil by thefield B₁. After each pulse of field B₁, the RF field produced by therotating magnetization M induces a voltage V in the RF coil. The inducedvoltage produces a current I=V/Z in the RF coil, where Z is theimpedance of the RF coil. The current I flowing in the RF coil thenproduces an induced RF magnetic field B₂. FIG. 13C shows the form of aB₂ field that can be produced in an embodiment of the invention. The B₂field shown in FIG. 13C is positive for the early pulses because theimpedance of the RF coil is adjusted accordingly. The B₂ field shown inFIG. 13C is zero for the later pulses because the RF coil is decoupled.Adjustment of the impedance Z of the RF coil alters the induced magneticfiled B₂ for the same static magnetic field B_(o), the same samplematerial, and the same excitation RF magnetic field B₁. Adjustment ofthe impedance of the RF coil can be accomplished by adjusting theresistance of the RF coil.

The means for detecting the net RF field over the region of interest canthen measure the net RF field B_(net). This means for detecting B_(net)can be, for example, one or more receive coils. A voltage is produced ineach receive coil due to B_(net) to produce a portion of a MRI signal.When the RF coil is not decoupled, B_(net) is the vector sum of B_(M)and B₂, after exciting the sample material with excitation field B₁,where B_(M)=μ_(o)M, M is the rotating magnetization of the sample andμ_(o) is the magnetic permeability of free space. When the RF coil isdecoupled, B_(net) is B_(m) after exciting the sample material. In anembodiment, excitation field B₁ can be delivered in pulses separated byperiods where B₁ is turned off, such that the net RF field can bemeasured between adjacent pulses of excitation field B₁. The means fordetecting can then provide a first portion of an MRI signal when B₂ isnon-zero and a second portion of the MRI signal when the RF coil isdecoupled (or has very high impedance) and B₂ is zero. These twoportions of the MRI signal can then be used to produce simulated fMRIdata. In a specific embodiment, the second portion of the MRI signal canresult from detection of B_(net) when B₂ is non-zero and the impedanceof the RF coil has been adjusted with respect to the detection ofB_(net) to produce the first portion of the MRI signal, in contrast todecoupling the RF coil during the production of the second portion ofthe MRI signal.

The resulting simulated fMRI data can be compared with the knownexcitation pattern to analyze the simulated fMRI data. In specificembodiments, the simulated fMRI data includes a portion of a MRI signalwhen the RF coil is decoupled, representing no stimulation of thesimulated patient and a portion of the MRI signal when the RF coil isnot decoupled representing stimulation of the simulated patient. As inactual fMRI measurements, various permutations of stimulation and nostimulation can be utilized. For example, the stimulation can be pulsed.

In a specific embodiment, the RF coil is positioned parallel to thestatic magnetic field B_(o) such that the RF coil is associated with anRF magnetic field that is perpendicular to the static magnetic field.Stated another way, for an embodiment using a planar coil, the normal ofthe plane of the coil is perpendicular to the static magnetic field.Although it is preferred to used RF coils associated with RF magneticfields, perpendicular to the static field B_(o), RF coils positioned atan angle to the static magnetic field B_(o) can also be utilized. Ofcourse, with most RF coils the direction of the associated magneticfield changes as a function of position, such that the relativedirection of the static field B_(o) and the associated magnetic fieldchanges with position as well. In this way, the relative directions ofthe associated field and the static field B_(o) may be perpendicularover a certain region. In an embodiment, this can be considered theregion of interest.

One or more additional RF coils can also be positioned proximate thesample material in much the same way as the first RF coil. Preferably,an additional RF coil is at an angle with respect to first RF coil, suchthat the additional RF coil is associated with an RF magnetic field thathas a component perpendicular to the static magnetic field andperpendicular to the component of the first RF coil that isperpendicular to the static magnetic field. For example, if the staticmagnetic field is parallel to the Z-axis and the first RF coil isassociated with an RF magnetic field having a component in the Xdirection, the additional RF coil preferably is associated with an RFmagnetic field having a component in the Y direction. If the first RFcoil and the additional RF coil are planar, another description is thatthe normal to the plane of the first RF coil has a component in the Xdirection and the additional RF coil has a component in the Y direction.A most preferred embodiment involves two planar RF coils that are bothparallel to the static magnetic field and the normals to the planes ofthe two RF coils are perpendicular to each other. Although planar coilsmay be preferred in some applications, a variety of RF coils can beutilized, including, but not limited to the following: Aldermann-Grant,Helmholtz, ring, square, rectangular, and birdcage.

The subject invention also pertains to the incorporation of one or morecoils for producing dc magnetic fields parallel to the static magneticfield B_(o). Such dc field coils can be used in conjunction with one ormore RF coils as discussed above or can be used without the RF coil(s).Preferably the dc field coil is associated with a dc field parallel toB_(o) in the region of interest. Most preferably, the dc field coil is aplanar coil having a normal perpendicular to B_(o). The dc field coil(s)then change the net static field experienced by the sample materiallocated in the region of interest. Although it is described as changingthe static field, it is understood that the dc current driving the dccoil can be made to vary such that the static field in the direction ofB_(o) is in fact a dynamic field. In fact, the dc coil(s) can be drivenwith dynamically varying currents that include a model of one or morephysiological functions, or other conditions to be modeled, such aspatient's breathing. Again, the strength and direction of the magneticfields associated with the dc coil(s) varies with position so that thedc coil(s) changes the field in the direction of the static field B_(o)as a function of position.

For example, if the static field coil produces a static field componentin the direction parallel to B_(o) of B_(s), then the net static fieldin the direction parallel to B_(o) is B_(o)+B_(s), if B_(S) is in thesame direction as B_(o), and B_(o)−B_(S), if B_(S) is in the oppositedirection of Bo. This change in the static field can alter the T2*relaxation of by the sample material and, therefore, the resultingmagnetic field B_(M) of the rotating magnetization M, where T2*characterizes the decay of the transverse component of the magnetizationafter excitation. FIGS. 14A-C show an excitation field B₁, the resultingmagnetic field B_(M) of the rotating magnetization M, and the DC currentthat can drive a coil for producing a static magnetic field parallel tothe direction of B_(o), respectively, in accordance with an embodimentof the subject invention. In a further embodiment, the excitation ofFIG. 14A and the DC current of FIG. 14C can be applied to the embodimentof FIG. 11 having only one DC loop.

A variety of sample materials can be utilized in accordance with thesubject invention. The sample material can be chosen to have magneticproperties of another object or material such as a human brain, a humanheart, and/or a human bone. In a specific embodiment, a gel, such as anagarose gel, can be used. The gel can incorporate substances which alterits properties. An example includes an agarose gel with copper sulfate.In this example, the concentrations of agarose and copper sulfate can beadjusted to match a particular material such as human brain tissue. In aspecific embodiment, the sample material can be selected so as to have aT1 value, T2 value, and/or T1/T2 ratio in a certain range. All or aportion of the sample material can also be moved during the productionof the simulated fMRI data. Such motion can be periodic, if desired, soas to model, for example, breathing. In additional embodiments, thesample material can flow through a conduit during the production of thesimulated fMRI data. Such flowing of the sample material can be used to,for example, model blood flow. The properties of the flowing samplematerial can be adjusted during the production of the fMRI data. Thiscan be utilized to model a dynamically changing model material. One ormore of the RF coils and/or static field coils can be moved duringproduction of the simulated fMRI data. The shape of the sample materialcan also be changed to model a certain object and/or material. Forexample, a cavity within the sample material can be expanded andcontacted during the production of stimulated fMRI data and/or thesample material can be expanded and/or contracted. In an embodiment, oneor more RF shields can be incorporated to shield some of the samplematerial from the magnetic field B₂ and/or from the excitation field B₁,in order to assist in the creation of a known enhancement pattern withknown characteristics.

Preferably, the sample material has a high proton density and a T2relaxation that is long enough to provide sufficient stimulated fMRIdata, where the T2 relaxation time characterizes the decay of thetransverse component of the magnetization caused by spin-spininteraction after excitation. A gel having water can be used and canhave additives to adjust the T2 and T1 of the gel in order to have thedesired properties. In an agarose gel, copper sulfate can be used toadjust the T1. Human brain grey matter has a T1 and T2 of approximately1000 ms and 90 ms, respectively. The sample material can also be waterdoped with different ions, oils, and/or organic material such aspolyvinyl alcohol so as to have T1 and/or T2 comparable to a desiredtissue to model, such as a human brain.

In a specific embodiment, the subject invention pertains to a functionalmagnetic resonance imaging (fMRI) activation simulator and a method ofproviding simulated fMRI activities. The subject fMRI activationsimulator can generate simulated functional changes based on known,controllable signal input. When placed in an MRI scanner the subjectphantom can produce calibrated and repeatable fMRI activities, so as topermit an objective, systematic comparison of fMRI analysis methods. Thecontrollable signal input can allow such factors as hemodynamic delay tobe taken into account, and can allow control of the shape of the outputsignal so as to, for example, control contrast.

The subject phantom can simulate various hemo-dynamic response models,smoothing and delay, and cardiac and respiratory “noise”. The subjectphantom can simulate the neural activation signal and produce a signalintensity change resembling the physiological data. The subject phantomcan provide a means to characterize, validate, and compare informaticstools, as well as be used for MRI quality control.

FIGS. 1A-1C shows an embodiment of the subject smart phantomincorporating two planar rectangular RF probes/coils 2, 3 placed into acylinder 4. FIG. 1A shows the probes 2, 3 during insertion into cylinder4. Excitation of the RF coils induce magnetic field changes and thusproduce regions of variable MR image contrast to noise. The excitationof the RF coils can be under the control of a computer. The RF coils canbe oriented such that the magnetic field associated with driving acurrent through the RF coil has a component perpendicular to the mainstatic magnetic field of the MRI MR scanner into which the subjectphantom is placed. Stated another way, the normal to the plane of theplanar RF coils has a component perpendicular to the main staticmagnetic field B_(o). In the embodiment shown in FIGS. 1A-1C, the RFprobe is a quadrature secondary coil, having two planar rectangularloops in parallel with the static magnetic field, such that the normalof each of the planes associated with the planar loops is perpendicularto the main static magnetic field B_(o). In the embodiment of FIGS.1A-1C, the two planar loops are placed at a 90 degree angle with respectto each other. In alternative embodiments, the two loops can be placedat other angles with respect to each other or can be parallel to eachother. In the embodiment shown in FIGS. 1A-1C, the two loops are planarrectangular and are positioned to form an inner cylinder 8, where theinner cylinder 8 shown in FIGS. 1A-1C in outline form. Sample materialcan be placed inside the inner cylinder 8 of the subject phantom insufficient proximity to the RF coils that the rotating magnetization ofthe sample material can reach the RF coils so as to have a meaningfulimpact on the MRI measurements. In a specific embodiment, a containerhaving a sample material can be located such that at least a portion ofthe sample material is located within the inner cylinder 8 formed by thesurface loops. In an embodiment, the sample material can be locatedwithin a cylindrical container and the cylindrical container can beplaced inside the two loops.

Referring to the embodiment shown in FIGS. 1A-1C, the two planarrectangular loops travel up the outside of the structure from the bottomand the travel toward the central axis of the inner cylinder 8 at thetop of the inner cylinder formed by the loops, leaving the top portion 6to house the circuitry of the loops, which can be used to, for example,control the impedance of the loops.

A schematic diagram of a specific embodiment of a loop in accordancewith the subject invention is shown in FIG. 2. In this embodiment, thediode symbol represents a PIN diode. During transmit, or excitation ofthe sample material with excitation RF magnetic field B₁ by the MRScanner, the PIN diodes D₁, D₂, D₃, and D₄ can be reverse biased suchthat no current flows in the circuit, such that the RF coil isdecoupled. During receive, or collection of data by the MR Scanner, theresistors of the resistor array can be switched in and out, by turningon and off each individual PIN diode. The resistor array can becontrolled so as to adjust the impedance of the RF coil in order toachieve a desired degree of signal enhancement. When a sample materialis placed in the static magnetic field of the MR Scanner and excitedwith an excitation RF magnetic field B₁, the magnetization of the samplematerial M will rotate. The rotating magnetization M induces a voltagein the RF coil, which induces a current to flow in the RF coil. Thecurrent flowing in the RF coil produces an induced magnetic field B₂. Inan embodiment, the loop can be tuned such that it is purely resistive atresonance. In an embodiment, the induced current can be 90 degrees outof phase with the applied magnetization, such that the signal from theloop and the signal from the sample material magnetization can be addedin quadrature. The control signal for controlling the impedance of theRF coil can be produced by computer simulation, which can provide, invarious embodiments, one or more of the following functions:

-   -   (1) A range of enhancement level (for example from 1% to 10%)        can be provided over regions of interest. Positive and negative        enhancement levels can be provided and, in an embodiment,        enhancement levels can between about 0.25% and about 10% can be        provided. Enhancement levels higher than 10% can also be        achieved.    -   (2) Typical hemo-dynamic waveforms (e.g., Boxcar, Gamma,        Gaussian) can be provided.    -   (3) Duty cycle (on-off duration) control can be provided, such        that each cycle can have a variable or fixed stimulus/on period        and a variable or fixed control/off period.

A synchronization signal (e.g., transmit unblank from MR scanner) can beutilized to start the computer sending the control signal, insynchronization with thee functional scan.

A diagram of a specific embodiment of a smart phantom implementationsystem in accordance with the subject invention is shown in FIG. 3. Apersonal computer (PC) can be used as a main control unit, which sendsout the control signals. In a specific embodiment, the signaltransmission between the PC (in the control room) and the subjectphantom (in the magnet room) can be done using fiber optics. A shieldedcontrol circuit board can be used to magnify the signal before it issent to the coils/probes in the subject phantom.

The subject invention can also be utilized to evaluate an algorithm foranalyzing fMRI data. In an embodiment, simulated fMRI data with a knownenhancement pattern can be provided, the simulated fMRI data can beanalyzed via an algorithm for analyzing fMRI data to create a predictionof the known enhancement pattern and the prediction of the knownenhancement pattern can be compared to the known enhancement pattern. Ina further embodiment, one or more parameters of the algorithm can beadjusted and the simulated fMRI data can be reanalyzed. The adjustedprediction of the known enhancement pattern can be compared to the knownenhancement pattern. The adjustment of parameters and comparisons can berepeated until the comparison indicates an effective match between theadjusted prediction and the known enhancement pattern is achieved. Ifdesired, the adjusted algorithm can then be utilized to analyze fMRIdata from a patient. In a specific embodiment, the method of evaluatingan algorithm for analyzing fMRI data can utilize simulated fMRI dataproduced via the use of the subject phantom as described herein.

There are many popular software packages that utilized methods foranalyzing fMRI data. We have compared SPM (statistical parametricmapping), FSL (FMRIB Software Library), and BrainVoyager™. Anotherexample of a software package that analyzes fMRI data is AFNI (Analysesof Functional Neuroimages).

There are a number of parameters that can be adjusted for each of thesepackages. In an embodiment, the subject smart phantom can be used toadjust the algorithm, by adjustment of parameters, to achieve anappropriate P value (a threshold that determines which voxel isactivated) of the statistical map. In an embodiment where the subjectphantom provides motion of the sample material, RF coils, DC coils,and/or the entire phantom, the best motion correction parameters, suchas basis choice and interpolation methods can be arrived at. In anembodiment where the phantom provides physiological noise, such asrespiratory and cardiac perturbation, the best parameters of temporalsmoothing can be arrived at.

Design Scheme I

In a specific embodiment, the subject phantom can provide four or moreRF probes/coils. In a further specific embodiment, each loop can beabout 2.5 cm×5 cm. In alternative embodiments, and RF coil has a maximumlength in at least one dimension of less than 4 cm. and/or a maximumlength in at least one dimension of less than one-third the maximumlength of the sample in the same dimension. Each RF loop can bestrategically placed in the phantom such that the magnetic fieldassociated with driving a current through the RF loop has at least acomponent perpendicular to the static magnetic field B_(o) of the MRscanner into which the subject phantom is placed. In an embodiment, theloop(s) can be placed parallel with the static magnetic field B₀. In anembodiment utilizing a head phantom, coils can be placed at positionsthat approximate the location of the primary visual cortex, the locationof the motor cortex, and the location of the auditory cortex. The probesact as local spin magnetization amplifiers and thus produce regions ofvariable MR image contrast to noise.

The control signal can be produced by a personal computer (PC), and canprovide, for example, the following functions:

-   -   (1) A range of enhancement level from, for example, 1-10% can be        modeled over each region of interest. In a specific embodiment,        enhancement levels of 0.25% -1% can be modeled as well. Positive        and/or negative enhancement levels can be produced, as can        enhancement levels higher than 10%.    -   (2) Typical BOLD modeling (Poisson, Gamma, Gaussian)

The fMRI time series signal (hemodynamic response) at time t due toneuronal activity x(t) (sensory or cognitive stimulation) is denoted byy(t), the coupling between the neuronal activity and hemodynamicresponse is given byy(t)=γx(t)·h(t)+n(t)   (1)where ‘·’ denotes convolution, γ denotes the gain of the fMRI imagingprocess and n(t) represents the noise. The h(t) is the hemodynamicmodulating function or hemodynamic “impulse response” of the BOLDsignal. The h(t) has been modeled as different functions, such as aPoisson function, a Gamma function, and a Gaussian function. Therefore,these, and/or other, functions can be employed in the BOLD signalmodeling for the phantom. The mathematical forms of these functions canbe represented as follows:

a. Poisson function $\begin{matrix}{{h(t)} = \frac{\lambda^{t}{\mathbb{e}}^{- \lambda}}{t!}} & (2)\end{matrix}$where λ represents the lag and dispersion.

b. Gaussian function $\begin{matrix}{{h(t)} = {\frac{1}{\sqrt{2\quad{\pi\sigma}^{2}}}{\exp( {- \frac{( {t - \mu} )^{2}}{\sigma^{2}}} )}}} & (3)\end{matrix}$where μ and σ are the mean and standard deviation (or lag anddispersion) of the function.

c. Gamma function $\begin{matrix}{{h(t)} = \frac{( {t/\tau} )^{n - 1}{\mathbb{e}}^{{- t}/\tau}}{{\tau( {n - 1} )}!}} & (4)\end{matrix}$where t is time, τ is a time constant, and n is a phase delay. A puredelay between stimulus onset and the beginning of the fMRI response isalso allowed. The pure delay here accounts for any systematic asynchronybetween stimulus onset and data acquisition and for any real delaybetween stimulus onset and hemo-dynamic response.

Most fMRI studies have been focused on neural activation analysis andhave showed the timing issue. As reviewed in Chapter 19 of Moonen &Bandettini (Eds.) (1999) Functional MRI, Springer-Verlag, withactivation, the time for the BOLD response to first significantlyincrease from baseline is approximately 2 s. The time to plateau in theon state is approximately 6-9 s. With cessation of activation, the timeto return to baseline is longer than the rise time by about 1 or 2 s.Several groups have reported a pre-undershoot or initial dip during thefirst 500 ms to 2 s of the signal. More commonly observed is apost-undershoot, which is observed more in visual cortex than in motorcortex and has an amplitude that is dependent on stimulus duration.

The control waveform of the subject smart phantom can be modeled toreflect the dynamic characteristics according to the research in theliterature. Duty cycle control can also be done through the waveformssent to the phantom. For example, the on-off duration can be from50%-50% to 10%-90%.

In a specific embodiment of the subject phantom, physiological “noise”,i.e., cardiac, respiratory, and brain (for example around 0.1 Hz)“noise” can be modeled and simulated.

Validation of the Subject Smart Phantom

The desired “answer” in blood oxygenation level dependent (BOLD) fMRI isdelineation of an enhancement region with the best confidence. Thesubject phantom can serve as a local signal enhancement model.

The following process can be used in accordance with the subjectinvention. A reciprocal view of the coil and phantom can be taken, sothat a given coil can be assumed to be driven. The field produced by theMR coil can be assumed constant over the secondary coils (in thephantom) surface area. An EMF can be calculated in the secondary coil.As an example, a simple loop can be used. This induced voltage is 90degrees out of phase with the source field (coil current). The impedanceof the secondary coil can be adjustable to limit the current. In aspecific embodiment, the secondary coil impedance can be primarily real,such that the induced current will be 90 degrees out of phase with thesource current. Therefore, the net field is the vector sum of B_(M) andB₂, where B_(M)=μ_(o)M, where M is the rotating component of themagnetization of the sample at detection and μ_(o) is the magneticpermeability of free space, and B₂ is the induced field. It should benoted that although the analysis described is performed using areciprocal approach, the secondary loop, or RF coil, is preferablydeactivated during transmit such that the enhancement of field describedapplies to the receive phase only. This enables a linear approach offield and sensitivity. Preferably, the RF coils impedence is increasedto a high enough value that negligible current flows during the transmitof the excitation magnetic field B₁, where the excitation field B₁ isturned on and off. When the excitation field is off, the impedence ofthe RF coil(s) can be lowered such that current can flow and stimulateddata can be measured. The impedence of the RF coil(s) can be adjusted ina time dependent manner, in order to, for example, model physiologicalprocesses.

Circuit Schematic and Impedance Control

Circuit schematics with respect to a specific embodiment of the subjectinvention are shown in FIGS. 4A and 4B. Each circuit has a conductorloop, and other components that are used to adjust the loop's impedance.The loop is tuned to the Larmor frequency of the magnet with a tuningcapacitor, such as C₀ or C₁. The area covered by the loop determines theRegion of Interest (ROI), where signal enhancement can be detected by areceive coil, such as a head coil. The signal enhancement is caused bycurrent induced from the sample magnetization during the receive phase.

MRI signals come from the magnetization of nuclei spins of the samplematerial. The rotation of the magnetization, after excitation of thesample material, induces current in the RF coil. This current in the RFcoil produces an induced magnetic field B₂ in the region of interest.This time-varying magnetic field B₂ penetrates the receive, ordetection, coil, and generates additional signal in the detector(receive coil) in superposition to the signal from spin magnetization.In the ‘off’ state, where the RF coil is decoupled, only B_(M) inducevoltages in the receive coil, resulting in V_(M). In the ‘on’ state,B_(net), instead of B_(M), will induce voltages in the receive coil,resulting in V_(net). Then we can define the enhancement level as:$\begin{matrix}{{enhancement} = {\frac{V_{net} - V_{M}}{V_{M}}.}} & (5)\end{matrix}$

By adjusting the impedance of the loop, which will be pure resistancewhen resonant, one can change the induced current, which is a ratio ofthe induced voltage over impedance. The induced current determines thesecondary, or induced, field B₂ and, therefore, the level ofenhancement, where the enhancement level is defined as$\frac{V_{net} - V_{M}}{V_{M}}.$

FIG. 4A shows an embodiment of a coil and accompanying circuitryimplementing impedance control using two LC resonance traps, inaccordance with the subject invention. Each trap includes an inductor, acapacitor, and a pin diode. The pin diode is a non-linear component,such that its forward resistance is a function of bias current. Theupper trap, including inductor L₁ and capacitor C₁, which are tuned toresonate at the Larmor frequency of the magnet, and diode D₁, produceshigh impedance during transmit so as to de-couple the resonance loopduring transmit. The lower trap, including the inductor L₂ and capacitorC₂, which are tuned to resonate at the Larmor frequency of the magnet,and diode D₂, produces adjustable impedance during receive. By adjustingthe bias current fed to diode D₂ through an adjustable resistor R, onecan change forward resistance of diode D₂, denoted as r. Therefore, theimpedance Z_(r) across capacitor C₂ is $\begin{matrix}{Z_{r} = \frac{X_{c}^{2}}{r}} & (6)\end{matrix}$where X_(c) is the reactance of capacitor C₂. Consequently the inducedcurrent as well as the enhancement is changed. Inductors L₃, L₄ canfunction as RF chokes.

FIG. 4B shows another embodiment of a coil and accompanying circuitryimplementing impedance control using a resistor array, composed ofresistors R₁, R₂ and R₃, in accordance with the subject invention. Eachresistor is in parallel with a corresponding diode and a correspondingdc-blocking capacitor such that resistor R₁ is in parallel with diode D₂and capacitor C₂, resistor R₂ is in parallel with diode D₃ and capacitorC₃, and resistor R₃ is in parallel with diode D₄ and capacitor C₄.Therefore, each resistor can be involved into the resonant loop if thecorresponding diode is off, and not involved in the resonant loop if thecorresponding diode is on. Diode D₁ is reverse-biased during transmit tode-couple the resonance loop. Inductors L₁ through L₄ can function as RFchokes.

Control of Loop Impedance

This section describes how to control the impedance of the resonanceloop in order to acquire different levels of enhancement. Referring toFIG. 4A, the impedance of the resonance loop can be controlled by using,for example, a resonance trap or a resistor array. Both of thesetechniques can incorporate pin diodes that can be biased to control theimpedance of the loop. Therefore, by adjusting the biasing current, onecan control the impedance of the loop. In the following, two specificimplementation methods in accordance with the subject invention, thatdetermine how to send a biasing current so as to control the impedanceof the loop, are shown.

1. Control Implementation of Resistor Array

In a specific embodiment, a personal computer (PC)'s serial port/RS232can be used to send a digital data stream to the subject phantom, asshown in FIG. 5. The data stream includes 1's and 0's, where, forexample, a 1 can turn on a diode in the circuitry of the embodimentshown in FIG. 4B so as to bypass the parallel resistor in the loop and a0 can turn off a diode in the circuitry of the embodiment shown in FIG.4B such that the parallel resistor is part of the loop impedance.

2. Control Implementation of High Impedance Trap

In another specific embodiment, a PC's parallel port, for example, asound card, can be used to send a continuous analog signal to thesubject phantom. The analog signal can provide a continuous current thatbiases the diode shown in the embodiment shown in FIG. 4A, which,consequently, controls the impedance of the loop.

Susceptibility Issues in Smart Phantom

Inhomogeneous B-Field and EPI Consideration

The subject phantom can be utilized with fMRI informatics. EPI imagingis used intensively in fMRI. EPI images are very sensitive tosusceptibility, which can be interpreted as two effects. The firsteffect is in-plane displacement and distortion caused by off-resonancein the image plane. The second effect is signal dropout due to fieldin-homogeneity perpendicular to the image plane. In an embodiment, thesubject phantom can be designed as a cylinder with gel inside. The fielddistortion can occur in both transverse direction and longitudinaldirection. The size of the phantom can be determined to optimize the EPIimage.

In the following, the theoretical issue will be addressed first. If wewriteH=−∇Ψ,   (7)where H is magnetic field intensity and Ψ is scalar magnetic potential.

Then, $\begin{matrix}{{{\nabla^{2}\Psi} = {- \frac{\rho_{m}}{\mu_{0}}}},} & (8)\end{matrix}$where ρ_(m) is magnetic charge density and μ₀ is permeability of freespace, where $\begin{matrix}{\rho_{m} = {{{- \nabla} \cdot ( {\mu_{0}\overset{harpoonup}{M}} )} = {{{- \nabla} \cdot ( {\frac{\chi}{1 + \chi}B} )} = {{- \frac{\mu_{0}^{2}}{\mu}}{\overset{harpoonup}{H} \cdot {\nabla\chi}}}}}} & (9)\end{matrix}$where {overscore (M)} is magnetization, χ is susceptibility, μ ispermeability of the material, and B is magnetic field flux density.

For a cylinder in another media, χ is constant except at the border, sowe obtain at point (r, θ, z), in cylindrical coordinates,$\begin{matrix}{\Psi = {\frac{\mu_{0}}{4\pi\quad\mu}{\int\limits_{S}{\frac{H_{0}{{\Delta\chi} \cdot \rho}}{\sqrt{r^{2} + \rho^{2} - {2r\quad\rho\quad{\cos( {\theta - \phi} )}} + z^{2}}}{\mathbb{d}\rho}{\mathbb{d}\phi}}}}} & (10)\end{matrix}$where S represents the surface of the top and bottom, ρ is an integralvariable for radius, φ is an integral variable for angle, and H₀ is theexternal magnetic field intensity.

The z component of H is $\begin{matrix}\begin{matrix}{H_{z} = {- \frac{\partial\Psi}{\partial z}}} \\{= {\frac{\mu_{0}}{4\pi\quad\mu}{\int\limits_{S}{\frac{{zH}_{0}{{\Delta\chi} \cdot \rho}}{( \sqrt{r^{2} + \rho^{2} - {2\quad r\quad\rho\quad\cos\quad( {\theta - \phi} )} + z^{2}} )^{3}}{\mathbb{d}\rho}{\mathbb{d}\phi}}}}}\end{matrix} & (11)\end{matrix}$

In this equation θ can be set to zero due to symmetry. Then,$\begin{matrix}\begin{matrix}{H_{z} = {- \frac{\partial\Psi}{\partial z}}} \\{= {\frac{\mu_{0}}{4\quad\pi\quad\mu}{\int_{s}^{\quad}{\frac{{zH}_{0}\Delta\quad{\chi \cdot \rho}}{( \sqrt{r^{2} + \rho^{2} - {2\quad r\quad\rho\quad\cos\quad\phi} + z^{2}} )^{3}}\quad{\mathbb{d}\rho}\quad{\mathbb{d}\phi}}}}}\end{matrix} & (12)\end{matrix}$Simulation

A simulation has been performed for a cylindrical phantom of fixedlength, L=20 cm, in z direction. The radius was set to 6 cm, 8 cm, and10 cm. These radii are consistent with practical situations. FIGS. 6Aand 6B show the field distortions in the radial and longitudinaldirections, respectively, for radii of 6 cm, 8 cm, and 10 cm. Referringto FIGS. 6A and 6B, for a fixed length cylinder, longitudinalinhomogeneity decreases with radius while transverse inhomogeneityincreases with radius. Therefore, there is essentially a tradeoffbetween the two susceptibility effects. Moving the curves to the samestarting point, within the vicinity of z=0 and r=0, the fieldinhomogeneity is essentially the same. The biggest change happens nearthe edge of phantom. Since the slices are chosen to be close to thecenter, it may be preferable to use a 6 cm radius phantom. FIGS. 6A and6B show field distortions in the radial and longitudinal directions,respectively, for a simulation of a cylindrical phantom of fixed lengthin the z direction.

FIGS. 7A and 7B show a comparison of the field distortions for threeradius by moving the curves in FIGS. 6A and 6B, respectively, tocoincide at r=0 or z=0.

With this design, high quality EPI images can be obtained.

FIGS. 8A and 8B show an EPI (SLT=5 mm, TE=54, FOV=160 mm) image and aSpin-echo image (same slice, TR/TE=552/16) of a specific embodiment ofthe subject smart phantom acquired in a Siemens Symphony system.

Gel Preparation

In an embodiment, the subject phantom can be filled partially, orcompletely, with a gel. Preferably, the gel in the phantom is chosen tomodel tissue to be imaged in the imaging system.

Some gels have bubbles, which can cause severe distortions of the EPIimage. In a specific embodiment, agarose gel can be used, due to theuniformity and stability of the agarose gel. The T1 and T2 of agarosegel can be controlled by adjusting the concentration of agarose andcopper sulfate, where T1 is longitudinal relaxation time and T2 istransverse relaxation time. Measurements of the T1 and T2 of agarose gelunder different concentrations of agarose and copper sulfate,respectively, were made. These measurements show that the inverse of T1and the inverse of T2 are proportional to the concentration of agarose(in pecentage) and the concentration of copper sulfate (in mM). In anembodiment of the subject invention, the following equations can be usedto model such relationships $\begin{matrix}{\frac{1}{T_{2}} = {{9.0 \times {10^{- 3}\quad\lbrack {{agarose}\quad\%} \rbrack}} + {2.10 \times {10^{- 3}\quad\lbrack {CuSO}_{4} \rbrack}} + {0.97 \times 10^{- 3}}}} & (13) \\{\frac{1}{T_{1}} = {{1.51 \times {10^{- 4}\quad\lbrack {{agarose}\quad\%} \rbrack}} + {9.433 \times {10^{- 4}\quad\lbrack {CuSO}_{4} \rbrack}} + {8.7 \times 10^{- 5}}}} & (14)\end{matrix}$To obtain a gel with a T1/T2 ratio in the range of a brain, for example,[CuSO₄]=0.75 mM and [Agarose]=1.2% can be chosen.Simulation of Respiratory Artifacts

The effect of respiration on fMRI imaging is usually considered assusceptibility changes due to breathing. According to Schenck (Schenck,J. The role of magnetic susceptibility in magnetic resonance imaging:MRI magnetic compatibility of the first and second kinds. Med. Phys. 23815-50, 1996), a spherical cavity induces a magnetic dipole field whichis given by $\begin{matrix}{{\Delta\quad{B( {x,y,z} )}} = \frac{\frac{1}{3}\Delta\quad\chi\quad B_{0}{R^{3}( {{2z^{2}} - x^{2} - y^{2}} )}}{( {x^{2} + y^{2} + z^{2}} )^{5/2}}} & (15)\end{matrix}$where R is the radius of the cavity, χ is susceptibility, and B₀ is theexternal magnetic field. This additional field change can be generatedby a small loop perpendicular to the magnetic field placed at the sameposition. $\begin{matrix}{{{{{B_{z}( {x,y,z} )} = {\frac{I\quad\pi\quad a^{2}}{c}\frac{( {{2z^{2}} - x^{2} - y^{2}} )}{( {x^{2} + y^{2} + z^{2}} )^{5/2}}\quad{for}\quad z}}}a},} & (16)\end{matrix}$where a is the radius of the loop, I is the current flowing in the smallloop, and c is the speed of light. This field is very small compared toB₀, therefore, it can be assume that the transverse field will notaffect the spins at all. However, we do not want to place the loop faraway from the phantom, such that the field distortion becomes slightlydifferent. The above equation can be rewritten as $\begin{matrix}{{B_{z}( {x,y,z} )} = {\frac{I\quad\pi\quad a^{2}}{c}\frac{( {{2z^{2}} - r^{2}} )}{( {r^{2} + z^{2}} )^{5/2}}}} & (17)\end{matrix}$where r is the distance between the imaged pixel and the center of theimaging slice. It is known that the susceptibility has two in-planeeffects. One effect is shift of the whole image and another effect isdistortion of the image. The shift of the whole image is due to thefield difference to B₀, the distortion is due to the field differencewithin the subject. In an embodiment of the subject phantom, z is about10 cm, while for a human body, z is about 35 cm. The induced fieldchange is computed from the above equation (18) for r up to 5 cm. Theresults are shown in FIGS. 9A and 9B.

FIGS. 9A and 9B show the field distortion for z=10 cm and z=35 cm,normalized at r=0 and the field distortion for z=10 cm and z=35 cm,scaled to make the overall change from r=0 to r=5 close to each other,respectively.

Referring to FIGS. 9A and 9B, both shift and distortion of the imagecannot be simulated simultaneously. However, the shift of the image canbe corrected by motion correction, such that this effect is notcritical. In an embodiment, the respiratory effect can be simulatedreasonably well by regulating the current in the additional loop of thesubject phantom in a rhythm consistent with breathing.

In an embodiment, the gradient field can induce emf in this loop, and$\begin{matrix}{{e\quad{mf}} = {\frac{\mathbb{d}\Phi}{\mathbb{d}t} \sim {\frac{\Delta\quad B}{\Delta\quad t}{S_{loop}.}}}} & (18)\end{matrix}$

However, for an EPI image, the effect of the gradient field can beneglected because the z-gradient only happens once for each slice and ittypically only affects the first few lines of k-space.

An embodiment of the subject smart phantom has been used to simulate aBlood Oxygenation Level Dependent (BOLD) signal in a real scan. In thisscan, 205 single-slice gradient echo EPI images were acquired in a GE1.5 T Signa scanner with a 4-channel phased array head coil (MRI DevicesCorporation, Waukesha, Wis., USA). The field of view (FOV)=16 cm, theRepetition Time (TR)=3 s and the Echo Time (TE)=31 ms. The imageMatrix=64×64, and the Slice Thickness (SLT)=3 mm. The first 5 imageswere discarded. The remaining images follow the paradigm of alternativeoff-on states, each of which lasts 30 s. The enhancement level of thephantom was set to 2%. The exams were repeated 3 times to get differentsignal-to-noise (SNR) ratios with Flip Angle (FA) equal to 90°, 30°, and12°. FIG. 10A is an EPI image of an axial slice of the subject phantom.The spin-like signal enhancement is supposed to be localized to thecenter of the circle and uniform in this region. Therefore, all theanalyses are chosen to be constrained on the 9-pixel square region ofinterest (ROI). FIG. 10B shows the BOLD-similar time course of the meansignal in the ROI for two enhancement levels. Besides signal variationfrom one time point to another, slight signal drift is also observed inthe 10 minutes scan.

Design Scheme II

In a specific embodiment, a coil loop can be positioned perpendicular tothe magnetic field B₀, such that DC current inported into the loop willproduce field distortion to B₀, where the distortion decays withdistance from the loop. In other embodiments, one or more coilsassociated with a magnetic field having a component parallel with staticfield B_(o) can be utilized. The coil(s) can be positioned above, below,and/or within the sample material. The incorporation of coil(s)providing fields in the B_(o) direction can be in conjunction with theuse of RF coils as described associated with magnetic fieldsperpendicular to B_(o), or can be used without such RF coils. The fielddistortion can affect the image in two ways. The field distortion cancause a global shift of the image due to B₀ offset. The field distortioncan also cause signal loss due to the gradient of field distortion in B₀direction, which can be used for simulating BOLD effect. The globalshift can be compensated for both active and basal states in BOLDimaging by, for example, using a phantom of cylinder shape with a loopattached to each end, where the axis of the cylinder intersects with thecenters of the two loops. FIG. 11 shows an embodiment of the subjectphantom having a cylindrical shape and having a loop attached to eachend of the phantom such that the axis of the cylinder intersects thecenters of the two loops. In a specific embodiment, a plurality of DCcoil loops can be positioned and provided with current to produce asubstantially constant B-field over the region of interest.

Referring to FIG. 11, a DC current can be input to one or both of theend loops to induce local field distortion, which simulatessusceptibility effect as BOLD. Diodes can be used to control on and offstates. In an embodiment, the ‘on’ state can be such that both loopshave currents and the ‘off’ state can be such that only one loop hascurrent, but of 2 times magnitude. The field of the ‘off’ state in thisembodiment is more inhomogeneous in z direction than the field of the‘on’ state, but the offsets of the z component of the magnetic field arealmost the same. The embodiment shown in FIG. 11 can be operated in amode that is T2-dependent. In theory, the coupling between the end loopsand receiver coils is small and, therefore, it should not introduce muchnoise, which is verified by experiments.

Referring to the embodiments shown in FIG. 11, two solenoids (10-turnloops, 2 cm in diameter) were put on the ends of a phantom in accordancewith the subject invention, with the axes of the end loops along B_(o)direction. For the ‘on’ state, 300 mA current was driven to bothsolenoids, and 60 images were acquired. For the ‘off’ state, 600 mAcurrent was driven to only one solenoid, and 60 images were acquired.FIG. 12 shows a difference image from the ‘on’ state (with current inboth loops) to the ‘off’ (with two times current in only one loop),after averaging. In FIG. 12, the center of mass shifts upward due tofield superposition. If we change the direction of the current, thiseffect can be, at least, partially corrected.

Other embodiments utilizing one or more coils as shown in FIG. 11 candrive the coils with a time varying current, in order to modeltime-varying activities. In a specific embodiment, the coil(s) can bedriven by a time-varying current that models breathing.

All patents, patent applications, provisional applications, andpublications referred to or cited herein are incorporated by referencein their entirety, including all figures and tables, to the extent theyare not inconsistent with the explicit teachings of this specification.

It should be understood that the examples and embodiments describedherein are for illustrative purposes only and that various modificationsor changes in light thereof will be suggested to persons skilled in theart and are to be included within the spirit and purview of thisapplication.

1. A method for producing simulated fMRI data, comprising: locating anRF coil in a static magnetic field B_(o), wherein the RF coil isassociated with an RF magnetic field such that the RF magnetic field hasa component that is perpendicular to the static magnetic field B_(o) ina region of interest; locating a sample material in a region of interestin the static magnetic field B_(o) such that the RF coil is proximate tothe sample material; exciting the sample material with an excitation RFmagnetic field B₁, which has a component perpendicular to the staticmagnetic field B_(o), such that the magnetization M of the samplematerial rotates; detecting a net RF magnetic field B_(net) in theregion of interest after exciting the sample material with theexcitation RF magnetic field B₁, wherein the rotation of themagnetization M of the sample material induces a voltage V in the RFcoil, wherein the voltage induced in the RF coil produces a current I,where ${I = \frac{V}{Z}},$ where Z is the impedance of the RF coil,wherein the current I produces an induced RF magnetic field B₂, whereinthe induced RF magnetic field B₂ alters the net RF magnetic fieldB_(net) proximate to the RF coil, wherein the net RF magnetic fieldB_(net) after exciting the sample material with the excitation RFmagnetic field B₁ is the vector sum of the magnetic field B_(M) of therotating magnetization M, where B_(M)=μ_(o)M and μ_(o) is the magneticpermeability of free space, and the induced RF magnetic field B₂,wherein a first portion of an MRI signal is produced for the region ofinterest; exciting the sample material with the excitation RF magneticfield B₁, which has a component perpendicular to the static magneticfield B_(o), such that the magnetization M of the sample materialrotates; detecting the net RF magnetic field B_(net) in the region ofinterest after exciting the sample material with the excitation RFmagnetic field B₁ and while the RF coil is decoupled, wherein the net RFmagnetic field B_(net) after exciting the sample material with theexcitation RF magnetic field B1 and while the RF coil is decoupled isthe magnetic field B_(M) of the rotating magnetization M, wherein asecond portion of an MRI signal is produced for the region of interest;and producing simulated fMRI data for the region of interest from thefirst portion of the MRI signal and the second portion of the MRIsignal.
 2. The method according to claim 1, wherein the excitation RFmagnetic field B₁ is perpendicular to the static magnetic field B_(o).3. The method according to claim 1, further comprising: decoupling theRF coil during exciting the sample material with an excitation RFmagnetic field B₁.
 4. The method according to claim 1, wherein excitingthe sample material with the excitation RF magnetic field B₁ comprisesexciting the sample material with the excitation RF magnetic field B₁via an MR scanner and detecting the net RF magnetic field in the regionof interest comprises detecting the net RF magnetic field in the regionof interest via the MR scanner.
 5. The method according to claim 4,wherein exciting the sample material with an excitation RF magneticfield B₁ via an MR scanner comprises applying a plurality of excitationRF magnetic field B₁ pulses.
 6. The method according to claim 1, whereinthe RF coil is rectangular.
 7. The method according to claim 1, whereinthe RF coil is sufficiently proximate to the sample material thatexcitation of the sample material produces a positive enhancement levelin at least a portion of the region of interest.
 8. The method accordingto claim 1, wherein the RF coil is sufficiently proximate to the samplematerial that excitation of the sample material produces a negativeenhancement level in at least a portion of the region of interest. 9.The method according to claim 1, wherein the RF coil is sufficientlyproximate to the sample material that excitation of the sample materialcan produce an enhancement level of at least 0.25% in at least a portionof the region of interest.
 10. The method according to claim 1, whereinthe impedance of the RF coil is approximately real.
 11. The methodaccording to claim 7, wherein the enhancement level is defined as$\frac{V_{net} - V_{M}}{V_{M}}$ where V_(net) is the voltage produced ina receive coil during detecting the net RF magnetic field B_(net) whenB_(net) is the vector sum of B_(M) and B₂, where V_(M) is voltageproduced in a receive coil during detecting the net RF magnetic fieldB_(net) while the RF coil is decoupled and B_(net) is BM.
 12. The methodaccording to claim 8, wherein the enhancement level is defined as$\frac{V_{net} - V_{M}}{V_{M}}$ where V_(net) is the voltage produced ina receive coil during detecting the net RF magnetic field B_(net) whenB_(net) is the vector sum of B_(M) and B₂, where V_(M) is voltageproduced in a receive coil during detecting the net RF magnetic fieldBnet while the RF coil is decoupled and Bnet is BM.
 13. The methodaccording to claim 9, wherein the RF coil is sufficiently proximate tothe sample material that excitation of the sample material produces anenhancement level of between about 1% and about 10% in at least aportion of the region of interest.
 14. The method according to claim 1,further comprising: locating a second RF coil in the static magneticfield B_(o), wherein the second RF coil is associated with a second RFmagnetic field such that the second RF magnetic field has a componentthat is perpendicular to the static magnetic field B_(o), wherein thesecond RF coil is proximate the sample; and decoupling the second RFcoil during detecting the net RF magnetic field B_(net) in the region ofinterest after exciting the sample material with the excitation RFmagnetic field B1 and while the RF coil is decoupled, wherein afterexciting the sample material with an excitation RF magnetic field B₁ therotation of the magnetization M of the sample material induces a secondvoltage V₂ in the second RF coil, wherein the second voltage induced inthe second RF coil produces a second current I₂, where${I_{2} = \frac{V_{2}}{Z_{2}}},$ where Z₂ is the impedance of the secondRF coil, wherein the second current produces a second induced RFmagnetic field B₃, wherein the second induced RF magnetic field B₃alters the net RF magnetic field B_(net) proximate to the second RFcoil, wherein the net RF magnetic field B_(net) after exciting thesample material with the excitation RF magnetic field B₁ is the vectorsum of the magnetic field B_(M) of the rotating magnetization M, theinduced RF magnetic field B₂, and the second induced RF magnetic fieldB₃, wherein the first portion of the MRI signal produced for the regionof interest includes the effect of the second induced RF magnetic fieldB₃.
 15. The method according to claim 1, wherein the RF coil has amaximum length in at least one dimension of less than about 4 cm. 16.The method according to claim 1, wherein the RF coil has a maximumlength in at least one dimension of less than one-third the maximumlength of the sample in the same dimension.
 17. The method according toclaim 1, wherein the RF coil is located within the sample material. 18.The method according to claim 1, further comprising adjusting the RFcoil resistance of the RF coil after exciting the sample material withthe excitation RF magnetic field B₁, wherein adjusting the RF coilresistance varies the enhancement level after exciting the samplematerial with the excitation RF magnetic field B₁.
 19. The methodaccording to claim 18, wherein the enhancement level is varied betweenabout 1% and about 10%.
 20. The method according to claim 1, wherein atleast a portion of the sample material moves during detecting the net RFmagnetic field B_(net) in the region of interest.
 21. The methodaccording to claim 20, wherein the at least a portion of the samplematerial flows during detecting the net RF magnetic field B_(net) in theregion of interest.
 22. The method according to claim 1, wherein atleast one property of the sample material is adjusted during detectingthe net RF magnetic field B_(net) in the region of interest.
 23. Themethod according to claim 1, wherein the RF coil is moved duringdetecting the net RF magnetic field B_(net) in the region of interest.24. The method according to claim 1, wherein the shape of the samplematerial is altered during detecting the net RF magnetic field B_(net)in the region of interest.
 25. A method for evaluating an algorithm foranalyzing fMRI data, comprising: providing simulated fMRI data, whereinthe provided fMRI data has a known enhancement pattern; analyzing thesimulated fMRI data via an algorithm for analyzing fMRI data to create aprediction of the known enhancement pattern; comparing the prediction ofthe known enhancement pattern to the known enhancement level pattern inorder to evaluate the algorithm for analyzing fMRI data.
 26. The methodaccording to claim 18, further comprising: (a) adjusting parameters ofthe algorithm for analyzing fMRI data; (b) analyzing the simulated fMRIdata via the adjusted algorithm for analyzing fMRI data to createcorresponding adjusted prediction of the known enhancement pattern; (c)comparing the adjusted prediction of the known enhancement pattern tothe known enhancement pattern in order to evaluate the algorithm foranalyzing fMRI data; and repeating (a), (b), and (c) above until thecomparison of the adjusted prediction of the known enhancement patternindicates an effective match between the adjusted prediction of theknown enhancement pattern and the known enhancement level pattern. 27.The method according to claim 26, further comprising: analyzing fMRIdata from a patient via the adjusted algorithm for analyzing fMRI data.28. The method according to claim 25, wherein providing simulated fMRIdata, comprises: locating an RF coil in a static magnetic field B_(o),wherein the RF coil is associated with an RF magnetic field such thatthe RF magnetic field has a component that is perpendicular to thestatic magnetic field B_(o) in a region of interest; locating a samplematerial in a region of interest in the static magnetic field B_(o) suchthat the RF coil is proximate to the sample material; exciting thesample material with an excitation RF magnetic field B₁, which has acomponent perpendicular to the static magnetic field B_(o), such thatthe magnetization M of the sample material rotates; detecting a net RFmagnetic field B_(net) in the region of interest after exciting thesample material with the excitation RF magnetic field B₁, wherein therotation of the magnetization M of the sample material induces a voltageV in the RF coil, wherein the voltage induced in the RF coil produces acurrent I, where ${I = \frac{V}{Z}},$ where Z is the impedance of the RFcoil, wherein the current I produces an induced RF magnetic field B₂,wherein the induced RF magnetic field B₂ alters the net RF magneticfield B_(net) proximate to the RF coil, wherein the net RF magneticfield B_(net) after exciting the sample material with the excitation RFmagnetic field B₁ is the vector sum of the magnetic field B_(M) of therotating magnetization M, where B_(M)=μ_(o)M and μ_(o) is the magneticpermeability of free space, and the induced RF magnetic field B₂,wherein a first portion of an MRI signal is produced for the region ofinterest; exciting the sample material with the excitation RF magneticfield B₁, which has a component perpendicular to the static magneticfield B_(o), such that the magnetization M of the sample materialrotates; detecting the net RF magnetic field B_(net) in the region ofinterest after exciting the sample material with the excitation RFmagnetic field B₁ and while the RF coil is decoupled, wherein the net RFmagnetic field B_(net) after exciting the sample material with theexcitation RF magnetic field B1 and while the RF coil is decoupled isthe magnetic field B_(M) of the rotating magnetization M, wherein asecond portion of an MRI signal is produced for the region of interest;and producing simulated fMRI data for the region of interest from thefirst portion of the MRI signal and the second portion of the MRIsignal.
 29. The method according to claim 25, wherein the prediction ofthe known enhancement pattern is a prediction of the known enhancementpattern in time and space.
 30. The method according to claim 25, whereinthe known enhancement pattern is created by simulation.
 31. The methodaccording to claim 25, wherein the known enhancement pattern ismeasured.
 32. The method according to claim 25, wherein the knownenhancement pattern is created theoretically.
 33. The method accordingto claim 25, wherein the known enhancement pattern is created bystatistical analysis of a plurality of measurements of the enhancementpattern.
 34. The method according to claim 26, wherein the at least oneparameter adjusted allows achievement of an appropriate p value of thestatistical map.
 35. An apparatus for producing RF magnetic fields,comprising: an RF coil, wherein the RF coil is associated with an RFmagnetic field; a sample material, wherein the RF coil is proximate tothe sample material; and a means for decoupling the RF coils, whereinupon locating the RF coil in a static magnetic field B_(o), such thatthe RF magnetic field has a component that is perpendicular to thestatic magnetic field B_(o) and the sample material is in a region ofinterest, and exciting the sample material with an excitation RFmagnetic field B₁, which has a component perpendicular to the staticmagnetic field B_(o), such that the magnetization M of the samplematerial rotates, wherein the rotation of the magnetization of thesample material induces a voltage V in the RF coil, wherein the voltageinduced in the RF coil produces a current I, where ${I = \frac{V}{Z}},$where Z is the impedance of the RF coil, wherein the current produces aninduced RF magnetic field B₂, wherein the induced RF magnetic fieldalters the net RF magnetic field B_(net) proximate to the RF coil,wherein the net RF magnetic field B_(net) after exciting the samplematerial with the excitation RF magnetic field B₁ is the vector sum ofthe magnetic field B_(M) of the rotating magnetization M, whereB_(M)=μ_(o)M and μ_(o) is the magnetic permeability of free space, andthe induced RF magnetic field B₂, wherein upon decoupling the RF coilafter exciting the sample material with the excitation RF magnetic fieldB₁ the net RF magnetic field B_(net) is the magnetic field B_(M) of therotating magnetization.
 36. The apparatus according to claim 35, furthercomprising: a means for exciting the sample material with the excitationRF magnetic field B₁; and a means for detecting the net RF magneticfield B_(net) after exciting the sample material with the excitation RFmagnetic field B₁ to produce simulated fMRI data.
 37. The apparatusaccording to claim 36, further comprising: a means for adjusting theimpedance of the RF coil.
 38. The apparatus according to claim 37,wherein the means for adjusting the impedance of the RF coil comprises amans for adjusting the resistance of the RF coil.
 39. The apparatusaccording to claim 36, wherein the excitation RF magnetic field B₁ isperpendicular to the static magnetic field B_(o).
 40. The apparatusaccording to claim 35, wherein the RF coil is rectangular.
 41. Theapparatus according to claim 36, wherein the means for exciting thesample material with the excitation RF magnetic field B₁ comprises an MRscanner and the means for detecting the net RF magnetic field B_(net) toproduce simulated fMRI data comprises the MR scanner.
 42. The apparatusaccording to claim 36, further comprising: a means for decoupling the RFcoil during excitation of the sample material with the excitation RFmagnetic field B₁.
 43. The apparatus according to claim 36, wherein theRF coil is sufficiently proximate to the sample material that excitationof the sample material produces a positive enhancement level in at leasta portion of the sample material.
 44. The apparatus according to claim35, wherein the RF coil is sufficiently proximate to the sample materialthat excitation of the sample material produces a negative enhancementlevel in at least a portion of the sample material.
 45. The apparatusaccording to claim 35, wherein the at least one RF coil is sufficientlyproximate to the sample material that excitation of the sample materialcan produce an enhancement level of at least 0.25% in the samplematerial.
 46. The apparatus according to claim 35, wherein the impedanceof the RF coil is approximately real.
 47. The apparatus according toclaim 43, where the enhancement level is defined as$\frac{V_{net} - V_{M}}{V_{M}}$ where V_(net) is the voltage produced ina receive coil during detecting the net RF magnetic field B_(net) whenB_(net) is the vector sum of B_(M) and B₂, where V_(M) is voltageproduced in a receive coil during detecting the net RF magnetic fieldB_(net) while the RF coil is decoupled and B_(net) is B_(M).
 48. Theapparatus according to claim 44, where the enhancement level is definedas $\frac{V_{net} - V_{M}}{V_{M}}$ where V_(net) is the voltage producedin a receive coil during detecting the net RF magnetic field B_(net)when B_(net) is the vector sum of B_(M) and B₂, where V_(M) is voltageproduced in a receive coil during detecting the net RF magnetic fieldBnet while the RF coil is decoupled and B_(net) is B_(M).
 49. Theapparatus according to claim 35, further comprising a second RF coil,wherein the second RF coil is associated with a second RF magnetic fieldsuch that the second RF magnetic field has a component that isperpendicular to the static magnetic field B_(o), where the second RFcoil is proximate the sample material, wherein after exciting the samplematerial with the excitation RF magnetic field B₁, the rotation of themagnetization M of the sample material induces a second voltage V₂ inthe second RF coil, wherein the voltage induced in the second RF coilproduces a second current I₂, where ${I_{2} = \frac{V_{2}}{Z_{2}}},$where Z₂ is the impedance of the second RF coil, wherein the secondcurrent produces a second induced RF magnetic field B₃, wherein thesecond induced RF magnetic field alters the net RF magnetic fieldB_(net) proximate to the second RF coil, wherein the net RF magneticfield B_(net) after exciting the sample material with the excitationmagnetic field B₁ is the vector sum of the magnetic field B_(M) of therotating magnetization M, the induced RF magnetic field B₂, and thesecond induced RF magnetic field B₃.
 50. The apparatus according toclaim 35, wherein each of the RF coil has a maximum length in at leastone dimension of less than about 4 cm.
 51. The apparatus according toclaim 35, wherein each of the RF coil has a maximum length in at leastone dimension of less than one-third the maximum length of the sample inthe same dimension.
 52. The apparatus according to claim 35, wherein theRF coil is located within the sample material.
 53. The apparatusaccording to claim 35, further comprising a means for adjusting the RFcoil impedance.
 54. The apparatus according to claim 35, furthercomprising a means for adjusting the RF coil resistance of the RF coilafter exciting the sample material with the excitation RF magnetic fieldB₁.
 55. The apparatus according to claim 54, wherein adjusting the RFcoil resistance varies the enhancement level after exciting the RF coilsample material with the excitation RF magnetic field B₁.
 56. Theapparatus according to claim 54, wherein the enhancement level is variedbetween about 1% and about 10%.
 57. The apparatus according to claim 54,wherein the means for adjusting the RF coil resistance comprisessoftware control.
 58. The apparatus according to claim 35, wherein theRF coil acts as a local spin magnetization amplifier.
 59. The apparatusaccording to claim 49, wherein the RF coil and the second RF coil form aquadrature coil.
 60. The apparatus according to claim 59, wherein thesecond RF coil is orientated at angle with respect to the RF coil withrespect to a plane perpendicular to the static magnetic field B_(o). 61.The apparatus according to claim 60, wherein the second RF coil isorientated at an angle of about 90° with respect to the RF coil withrespect to the plane perpendicular to the static magnetic field B_(o).62. The apparatus according to claim 35, further comprising: at leastone additional coil associated with a corresponding at least oneadditional static magnetic field parallel to the static magnetic fieldB₀, where the at least one additional coil is located such that thecorresponding at least one additional static magnetic field associatedwith the at least one additional coil reaches the region of interest.63. The apparatus according to claim 62, wherein the at least oneadditional coil comprises two end coils positioned parallel to eachother, wherein at least a portion of the region of interest is betweenthe two end coils.
 64. The apparatus according to claim 60, wherein theRF coil and the second RF coil are both substantially planar, wherein acontainer having the sample material inside is positioned such that atleast a portion of the container is positioned to intersect the plane ofthe RF coil and to intersect the plane of the second RF coil.
 65. Theapparatus according to claim 64, wherein the container is positionedwithin a cylinder formed by the RF coil and the second RF coil.
 66. Theapparatus according to claim 65 wherein the container is cylindricallyshaped.
 67. The apparatus according to claim 36, wherein the means forexciting the sample material comprises a means for exciting the samplematerial with an excitation RF magnetic field B₁ that includes acharacteristic that models one or more physiological noises.
 68. Theapparatus according to claim 35, wherein excitation of the samplematerial produces regions of variable MR image contrast to noise. 69.The apparatus according to claim 36, wherein the means for exciting thesample material comprises a means to control the duty cycle of theexcitation.
 70. The apparatus according to claim 69, wherein the meansto control the duty cycle of the excitation allows variable and fixed onperiods and variable and fixed off periods.
 71. The apparatus accordingto claim 36, wherein the means for exciting the sample materialcomprises a means for exciting the sample material with an excitation RFmagnetic field B₁ that includes a characteristic that models ahemo-dynamic response.
 72. The apparatus according to claim 36, whereinthe means for exciting the sample material comprises a means forexciting the sample material with an excitation RF magnetic field B₁that includes a characteristic that models smoothing.
 73. The apparatusaccording to claim 36, wherein the means for exciting the samplematerial comprises a means for exciting the sample material with anexcitation RF magnetic field B₁ that includes a characteristic thatmodels delay.
 74. The apparatus according to claim 35, furthercomprising at least one additional RF coil.
 75. The apparatus accordingto claim 74, wherein the sample material models a human head, whereinone of the RF coil and the at least one additional RF coil is located ata position in the sample material that approximates the location of theprimary visual cortex.
 76. The apparatus according to claim 74, whereinthe sample material models a human head, wherein one of the RF coil andthe at least one additional RF coil is located at a position in thesample material that approximates the location of the primary motorcortex.
 77. The apparatus according to claim 74, wherein the samplematerial models a human head, wherein one of the RF coil and the atleast one additional RF coil is located at a position in the samplematerial that approximates the location of the primary auditory cortex.78. The apparatus according to claim 71, wherein the hemo-dynamicresponse is given by y(t)=γx(t)·h(t)+n(t), wherein “·” denotedconvolution, γ denotes the gain of the fMRI imaging process, and n(t)represents the noise.
 79. The apparatus according to claim 78, whereinh(t) is modeled as a Poisson function, where${{h(t)} = \frac{\lambda^{t}{\mathbb{e}}^{- \lambda}}{t!}},$ and λrespresents the log and dispersion.
 80. The apparatus according to claim78, wherein h(t) is modeled as a Gaussian function, where${h(t)} = {\frac{1}{\sqrt{2{\pi\sigma}^{2}}}{\exp( {- \frac{( {t - \mu} )^{2}}{\sigma^{2}}} )}}$and μ and σ are the mean and standard deviation.
 81. The apparatusaccording to claim 78, wherein h(t) is modeled as a Gamma function,where${{h(t)} = \frac{( {t/\tau} )^{n - 1}{\mathbb{e}}^{{- t}/\tau}}{{\tau( {n - 1} )}!}},$and t is time, τ is a time constant, and n is a phase delay.
 82. Amethod for producing simulated MRI data, comprising locating at leastone dc coil in a static magnetic field B_(o), wherein the at least onedc coil is associated with a corresponding at least one dc magneticfield such that each of the corresponding at least one dc magnetic fieldhas a component that is parallel to the static magnetic field B_(o);locating a sample material in a region of interest in the staticmagnetic field B_(o); driving the at least one dc coil with acorresponding at least one dc current so as to alter the magnetic fieldin the direction parallel to the static magnetic field B_(o); excitingthe sample material with an excitation RF magnetic field B₁, which has acomponent perpendicular to the static magnetic field B_(o), such thatthe magnetization of the sample material rotates; detecting a net RFmagnetic field B_(net) in the region of interest after exciting thesample material with the excitation RF magnetic field B₁, whereinB_(net) in the region of interest after exciting the sample material isthe magnetic field B_(M) of the rotating magnetization M, whereB_(M)=μ_(o)M and μ_(o) is the magnetic permeability of free space. 83.The method according to claim 82, further comprising: driving the atleast one dc coil with a corresponding at least one second dc current soas to alter the magnetic field in the direction parallel to the staticmagnetic field B_(o); exciting the sample material with the excitationRF magnetic field B₁, which has a component perpendicular to the staticmagnetic field B_(o), such that the magnetization of the sample materialrotates; detecting the net RF magnetic field B_(net) in the region ofinterest after exciting the sample material with the excitation RFmagnetic field B₁
 84. A method for producing simulated fMRI data,comprising: locating an RF coil in a static magnetic field B_(o),wherein the RF coil is associated with an RF magnetic field such thatthe RF magnetic field has a component that is perpendicular to thestatic magnetic field B_(o) in a region of interest; locating a samplematerial in a region of interest in the static magnetic field B_(o) suchthat the RF coil is proximate to the sample material; exciting thesample material with an excitation RF magnetic field B₁, which has acomponent perpendicular to the static magnetic field B_(o), such thatthe magnetization M of the sample material rotates; detecting a net RFmagnetic field B_(net) in the region of interest after exciting thesample material with the excitation RF magnetic field B₁, wherein therotation of the magnetization M of the sample material induces a voltageV in the RF coil, wherein the voltage induced in the RF coil produces acurrent I, where ${I = \frac{V}{Z}},$ where Z is the impedance of the RFcoil, wherein the current I produces an induced RF magnetic field B₂,wherein the induced RF magnetic field B₂ alters the net RF magneticfield B_(net) proximate to the RF coil, wherein the net RF magneticfield B_(net) after exciting the sample material with the excitation RFmagnetic field B₁ is the vector sum of the magnetic field B_(M) of therotating magnetization M, where B_(M)=μ_(o)M and μ_(o) is the magneticpermeability of free space, and the induced RF magnetic field B₂,wherein a first portion of an MRI signal is produced for the region ofinterest; adjusting the impedance of the RF coils; exciting the samplematerial with the excitation RF magnetic field B₁, which has a componentperpendicular to the static magnetic field B_(o), such that themagnetization M of the sample material rotates; detecting the net RFmagnetic field B_(net) in the region of interest after exciting thesample material with the excitation RF magnetic field B₁, wherein thenet RF magnetic field B_(net) after adjusting the impedance of the RFcoil and exciting the sample material with the excitation RF magneticfield B₁ is the vector sum of the magnetic field B_(M) of the rotatingmagnetization M and the induced RF magnetic field B₂, wherein a secondportion of an MRI signal is produced for the region of interest; andproducing simulated fMRI data for the region of interest from the firstportion of the MRI signal and the second portion of the MRI signal.